Question

the diagonal of a cuboid which is 5 metre long for 4 metre broad and 3 metre high find the total surface area lateral surface area and length ?​

Answer 1

Answer:

the diagonal of a cuboid which is 5 metre long for 4 metre broad and 3 metre high find the total surface area lateral surface area and length ?

Answer 2

Given : A cuboid which is 5 metre long for 4 metre broad and 3 metre high.

To Find : Find the total surface area of cuboid, Lateral surface area of cuboid & Diagonal of cuboid ?

_________________________

Solution : Length of cuboid (l) = 5m

$~~~~~~~~~~~~~~~~~$Breadth of cuboid (b) = 4m

$~~~~~~~~~~~~~~~~~$Height of cuboid (h) = 3m

$~$

◗Total surface area of cuboid

$\qquad{\sf:\implies{2\bigg(length ~×~breadth ~+~breadth ~×~height ~+~length ~×~height\bigg)}}$

$\qquad{\sf:\implies{2\bigg(lb~+~bh~+~lh\bigg)}}$

$\qquad{\sf:\implies{2\bigg(20~+~12~+~15\bigg)}}$

$\qquad{\sf:\implies{2\bigg(32~+~15\bigg)}}$

$\qquad{\sf:\implies{2~×~47}}$

$\qquad:\implies{\underline{\boxed{\frak{\blue{94~m^2}}}}}$★

$~$

• ${\sf\leadsto{\underline{Total ~surface~ area ~of ~cuboid ~is}~\bf{\underline{94~m^2}}}}$

$~$

◗Lateral surface area of cuboid

$\qquad{\sf:\implies{2\bigg(length~+~breadth\bigg)height}}$

$\qquad{\sf:\implies{2\bigg(l~+~b\bigg)h}}$

$\qquad{\sf:\implies{2\bigg(5~+~4\bigg)3}}$

$\qquad{\sf:\implies{2~×~9~×~3}}$

$\qquad{\sf:\implies{18~×~3}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{54~m^2}}}}}$★

$~$

• ${\sf\leadsto{\underline{Lateral~surface~ area ~of ~cuboid ~is}~\bf{\underline{54~m^2}}}}$

$~$

◗Diagonal of cuboid

$\qquad{\sf:\implies{D~=~\sqrt{l^2~+~b^2~+~h^2}}}$

$\qquad{\sf:\implies{D~=~\sqrt{(5)^2~+~(4)^2~+~(3)^2}}}$

$\qquad{\sf:\implies{D~=~\sqrt{25~+~16~+~9}}}$

$\qquad{\sf:\implies{D~=~\sqrt{25~+~25}}}$

$\qquad{\sf:\implies{D~=~\sqrt{50}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{D~=~7.07~m}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{Total ~surface~ area ~of ~cuboid~is~\bf{\underline{94~m^2}}}}$

$\therefore\underline{\sf{Lateral ~surface~ area ~of ~cuboid~is~\bf{\underline{54~m^2}}}}$

$\therefore\underline{\sf{Diagonal~of ~cuboid~is~\bf{\underline{7.07~m}}}}$